Gradient of a curve and differentiation from first principlesAQA A-Level Maths: Mind map

Exam questions on Gradient of a curve and differentiation from first principles

1. The curve $C$ has equation $y=x^2$. The point $P(3,9)$ lies on $C$, and $Q$ is the point on $C$ with $x$-coordinate $3+h$, where $h\neq0$.
   Find the equation of the tangent to $C$ at $P$.2 marks
2. The function $\mathrm{f}$ is defined by $\mathrm{f}(x)=x^3$.
   Find the coordinates of the points on the curve $y=\mathrm{f}(x)$ at which the gradient is 12.2 marks
3. The function $\mathrm{f}$ is defined by $\mathrm{f}(x)=3x^2-5x$.
   Prove from first principles that $\mathrm{f}'(x)=6x-5$.3 marks